Distance Formula
The distance dbetween and is
d 21 x 2 x 122 1 y 2 y 122.1 x 1 , y 12 1 x 2 , y 22 Find the distance between and.= 5
= 225
= 216 + 9
= 21 - 422 + 32
21 - 1 - 322 + 31 - 1 - 2242
1 3, - 22 1 - 1, 1 2
CONCEPTS EXAMPLES
CHAPTER 8 Summary 485
8.4 Adding and Subtracting Radical
Expressions
Only radical expressions with the same index and the
same radicand may be combined.
23 + 239
215 + 230
= 2727
= 14 - 9 + 32227
= 427 - 927 + 3227
= 2 # 227 - 3 # 327 + 8 # 427
= 224 # 7 - 329 # 7 + 8216 # 7
2228 - 3263 + 82112
8.5 Multiplying and Dividing Radical
Expressions
Multiply binomial radical expressions by using the FOIL
method. Special products from Section 5.4may apply.
Rationalize the denominator by multiplying both the
numerator and the denominator by the same expression,
one that will yield a rational number in the final
denominator.
To write a radical quotient in lowest terms, factor the
numerator and denominator and then divide out any
common factor (s).
5 + 1526
10
=
(^5) A 1 + (^326) B
5 # 2
=
1 + 326
2
=
(^4) A 25 + (^22) B
5 - 2
=
(^4) A 25 + (^22) B
3
4
25 - 22
=
(^4) A 25 + (^22) B
A 25 - 22 BA 25 + 22 B
27
25
=
27 # 25
25 # 25=
235
5
= 5 - 226
= 3 - 223 # 22 + 2
A^23 -^22 B
2= 5 - 10, or - 5A^25 -^210 BA^25 +^210 B
= 26 - 223 + 221 - 242 212 = 223
A^22 +^27 BA^23 -^26 B
(continued)cannot be
simplified further